Natural convection between two horizontal coaxial cylinders

The objective of our paper is to start the theoretical investigation of the most commonly used mathematical model for natural convection in a horizontal annulus. First, one shows existence of solutions for the unsteady problem. Then, for any Prandtl number and inverse relative gap width, existence, and stability of a steady solution is proved, provided that the Rayleigh number is sufficiently small. The same is also proved for any Rayleigh number provided the inverse relative gap width is sufficiently small. Furthermore, exponential decay to the steady symmetric solution and uniqueness hold true under stronger restrictions to the Rayleigh number. The objective of this paper is to start the theoretical investigation of the most commonly used mathematical model for natural convection in a horizontal annulus. First, one shows existence of solutions for the unsteady problem. Then, for any Prandtl number and inverse relative gap width, existence, and stability of a steady solution is proved, provided that the Rayleigh number is sufficiently small. The same is also proved for any Rayleigh number provided the inverse relative gap width is sufficiently small.